New research on old subject draws interest

Students are creating software to display the logical connections between the theorems of The Elements, a discourse on geometry.

Students at Penn State Harrisburg are gaining national attention from research they hope will bring new insights to the age-old study of geometry.

The group is creating software that displays the logical connections between the theorems of The Elements, the oldest written discourse on the study of geometry. The students are the first to extensively display these relationships using a visual technique, according to Dr. Eugene Boman, associate professor of mathematics, who is overseeing the project.

Siddharth Dahiya, of Camp Hill, and Tyler Brown, of Elizabethtown, both computer science and mathematical sciences double majors, received a Penn State Summer Discovery Grant for the project. The students, including Joseph Roberge, a graduate student in the Computer Science program, also received funding from Pi Mu Epsilon, the national mathematics honor society, and the college’s Mathematical Sciences program to complete their work, which began at the beginning of the year. Students Alexandra Milbrand, a mathematical sciences major, and Viplav Patel, a computer science major, also contributed significantly to the work. The students have presented their research in Madison, Wis. at MathFest, an annual nationwide mathematics conference, and at the regional Student Mathematics Conference at Moravian College, and will present at the Eastern Pennsylvania and Delaware sectional meeting of the Mathematical Association of America this fall.

The Elements, written in about 300 BC by Greek mathematician Euclid, begins by introducing five basic postulates, or foundational laws, that serve as the building blocks for later theorems. The students have gone through The Elements theorem by theorem, mapped out the connections between them, and written the software that displays these connections in a visual and interactive form.

“I’m very proud of the progress [the students] have made,” said Boman. “Last January we started with nothing but an idea and now we have a fairly sophisticated piece of software that displays Euclid’s work in a completely original manner. Every colleague I’ve shown this to has been impressed, and we’re not finished with it yet.”

The software can be altered to display the connections of any set of interconnected ideas, according to Boman, who said the program can be generalized for applications in industry as well as in science and mathematics.